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An electric motor takes $5 A$ from a $220 V$ line. Which of the following is the power of the motor and the energy consumed in $2 h$ ?

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7.9 \times 1 0^{6}

8.9 \times 1 0^{6}

6.9 \times 1 0^{6}

5.9 \times 1 0^{6}

answer is A.

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Detailed Solution

The power of the motor and the energy consumed in

2 h

is given by

7.9 \times 1 0^{6}

J.
Given data
Supplied voltage,

V = 220 V .

The current through the motor is,

I = 5 A .

The time of consumption is,

t = 2 h .

2 \times 60 \times 60 s = 7200 s

Power is the energy consumed by a body in a unit time.
In general, power,

E = P \times t

,
where

E

is the energy,

P

is the power, and

t

is the time.
Power is defined by the form,

P = V \times I

,
where

V

is the supplied voltage and

I

is the current through the circuit.
Calculation of power
As we know, power is

P = V \times I

So,

P = 220 \times 5

= 1100

P = 1100 watt .

Therefore, the power of the motor is

1100 watt

Calculation of energy consumption
We know that energy consumed by a body is,

E = P \times t

.
So,

\Rightarrow E = 1100 \times 7200

\Rightarrow E = 7920000 J

\Rightarrow E = 7.9 \times 1 0^{6} J

.
Therefore, the energy consumed in

2 h

by the motor is

7.9 \times 1 0^{6} J

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